This problem will be due to may reasons
>> Internet Explorer issue
>> Flash Player not properly installed
>> Browser not supporting the particular sites
1. If it is an issue with Internet Explorer steps to be done :
>> Reset the Internet Explorer For that :
-- Close all the Internet Explorer Windows
-- Click on Start ->Run then on the Run Box Type inetcpl.cpl Hit Enter
--New window opens
--Click On adwanced Tab , there click on Reset
--Now on Run Type temp hit Enter, then a Window will open Select all the files in that folder and delete
-- Then Again take the Run Window Type prefetch hit Enter, a Window will open then Select all the files in that folder and delete
-- Then again take Run Type %temp% hit Enter, a Window will open then Select all the files in that folder and delete
--Now try signing in Face book.
--Mostly issue will be resolved.
2. If Flash Player issue
--Go to this link download Flash player http://get.adobe.com/flashplayer/download/?installer=Flash_Player_10.3_for_Windows_Internet_Explorer&p=Google_Toolbar_6.5&a=Google_Chrome_8.0&os=Windows
-- Reastart the computer.
--Then issue may get fixed
3. If the Browser is not supporting
--Upgrade Internet Explorer
--Download other browsers
--Download Googole Chrome from this link http://www.google.com/chrome/index.html?hl=en&brand=CHNG&utm_source=en-hpp&utm_medium=hpp&utm_campaign=en
--Download Mozilla Fire Fox http://www.mozilla.com/en-US/firefox/all.html
Select the language then it will start downloading.
--Then use the new brwoser the issue will get fixed.